When flying between western Canada and England, it sometimes seems surprising that such a northward trajectory is followed. On my way back to Vancouver, for instance, we were treated to an aerial view of Iceland’s unique landscape. Of course, the reason for the path is that the spherical character of the earth is not well reflected in standard map projections. The most famous – the Mercator projection – is arranged such that a straight line drawn on the map will correspond to a course that actually passes through each point on the earth depicted. This kind of map is called ‘conformal.’ As such, the notorious distortion (enlarging the apparent size of polar regions while reducing that of equatorial ones) is an emergent property of its design.
That said, the most efficient course between any two points on the globe is probably not the one that connects them on a Mercator projection line of the shortest distance. Mathematically, the most direct course is based on what is called a ‘great circle.’ That is to say, imagine marking your present location and your destination using a marker on an orange. The line you could draw all the way around, intersecting both, is the great circle. The line segment between the points is the shortest distance that can be transcribed between them on a sphere (or near-sphere, in the case of the earth).
Unless you are going due north, due south, or straight around the equator, actually following a great circle path requires constantly changing your heading. This is because of how the line you are on does not maintain a constant bearing with respect to either magnetic or true north. In the days before computers and long haul air travel, few people would probably have bothered to calculate great circle courses. A more venerable option can be found in the Rhumb line. Now, GPS and autopilot systems have made doing so all but automatic. Hence the genesis of those gracefully arcing lines printed in your in-flight magazine.
On a separate note, the precision of modern location and navigation systems in aircraft can sometimes cause problems. (Via Philip Greenspun)